It's interesting that it's quite the opposite just over the river (200m walk say) where places like Tate Modern and around London Bridge are usually very busy indeed over the weekend.
There was one bonus - there is a shopping mall with lots of stores which stays open during the weekend, and is really quiet - I used to go there for last minute Christmas shopping at the weekend. When the rest of the country's shops would be packed, this entire mall was still very quiet, and open! I think it was near Cannon Street (One New Change, maybe?)
"The City of London is the only part of Britain over which parliament has no authority."
https://www.theguardian.com/commentisfree/2011/oct/31/corpor...
https://www.economist.com/britain/2001/08/02/the-mayors-new-...
https://www.ft.com/content/41dba03e-5d29-11e5-9846-de406ccb3...
It's truly unique place and I love it but one day I stayed at work till late and noticed that the place turned into a ghost town once the salarymen went home. Then went a few times cycling there in the weekend and I was astonished how empty it was. I actually enjoy solitude but the area is very business oriented and scared me away. Kind of regret not living there for a while, it would have been an experience.
Here are a few photos at the off hours, a bit too empty for a place that is extremely crowded at the day.
https://imgur.com/a/sgo7Yxe
edit: I particularly like this panorama image : https://imgur.com/a/yfh5hXN
At rush hour that location is so crowded that you can't walk without bumping into people but on the weekends you barely see people, even the tourists are not plenty despite being on a nice summer day.